Quenched Phonon Drag in Silicon Nanowires Reveals Significant Effect in the Bulk at Room Temperature

Abstract

Existing theory and data cannot quantify the contribution of phonon drag to the Seebeck coefficient (S) in semiconductors at room temperature. We show that this is possible through comparative measurements between nanowires and the bulk. Phonon boundary scattering completely quenches phonon drag in silicon nanowires enabling quantification of its contribution to S in bulk silicon in the range 25-500 K. The contribution is surprisingly large (∼34%) at 300 K even at doping of ∼3 × 10(19) cm(-3). Our results contradict the notion that phonon drag is negligible in degenerate semiconductors at temperatures relevant for thermoelectric energy conversion. A revised theory of electron-phonon momentum exchange that accounts for a phonon mean free path spectrum agrees well with the data.

High Seebeck Coefficient of Porous Silicon: Study of the Porosity Dependence

“…Boukai et al [ 7 ] studied highly doped individual Si nanowires of diameter 10 and 20 nm and reported an anomalous phonon drag enhancement at room temperature. A recent study on an array of Si nanowires with diameter ~100 nm and doping concentration ~10 19 cm −3 (surface roughness 0.4 nm) [ 30 ] contradicts the above and concludes that at 300 K, boundary scattering of phonons in the specific Si nanowires (which were highly doped) completely quenches drag and reduces S . If we now consider Si nanocrystals, recent studies [ 32 ] demonstrated experimentally that in quite small nanocrystals, of diameter 2.4 nm, the Seebeck coefficient was by one order of magnitude lower than in nanocrystals with sizes of 5.6 and 8.3 nm.…”

“…In bulk semiconductors at room temperature, the phonon drag effect is in general considered to be important in the case of the undoped or lightly doped material and smaller in the heavily doped material. Figure 8 shows some representative data from the literature [ 30 , 31 ] relating S , S d and S ph with doping concentration in the case of bulk Si. A large dependence of S on doping is observed.…”

“…8 Total Seebeck coefficient and contributions of S d and S ph in bulk c-Si at different carrier concentrations. S , S d and S ph were deduced from two different references in the literature [ 30 , 31 ] …”

Thermoelectric coefficients ofn-doped silicon from first principles via the solution of the Boltzmann transport equation

“…3,4 In addition to this, the role of the coupled electron-phonon dynamics on the thermoelectric properties of silicon has very recently attracted renewed interest. [11][12][13] Indeed, in this material there is a substantial enhancement, even at room temperature and in heavily doped samples, of the Seebeck coefficient induced by the drag exerted on charge carriers from phonons diffusing along a temperature gradient (phonon drag). In the past this topic has not received much attention beyond the initial experimental 14 and theoretical 15 works, but with current interest in thermoelectric energy conversion this effect might represent an interesting route to enhance thermoelectric performance.…”

Peak thermoelectric power factor of holey silicon films

“…The notion that phonon drag is suppressed in highly doped bulk samples stems partly from a conclusion reached by Weber and Gmelin 12 , who revisited the classic measurements of Geballe and Hull 24 with modifications of their own. Weber and Gmelin considered the low temperature (< 40 K) part 24 , Weber et al 12 , and Sadhu et al 11 ) for bulk silicon is shown for comparison. The dashed curves are theoretical calculations of the diffusion part of S assuming carrier concentrations listed in Table I. of their data for degenerately doped Si and claimed S ∼ T in that range.…”